论文标题
费米子的临界性是由费米表面拓扑塑造的：tomonaga-luttinger液体的案例研究
Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid
论文作者
论文摘要
我们对一维费米克哈伯德模型进行了单位重新归一化组（URG）研究。形式主义产生了一个有效的哈密顿量和多体征本系的家族，从UV到IR的整个张量网络上进行了全息。 URG被实现为量子电路，导致纠缠全息图（EHM）张量网络描述。表明，在费米表面的自由度的预测希尔伯特空间的拓扑$θ$ - 已显示出RG流向无质量的Tomonaga-Luttinger液体或间隙量子液相的性质。这导致了berezenskii-kosterlitz-thouless（BKT）RG相图的非扰动版本，揭示了一系列中间耦合稳定固定点的系列，而临界点周围RG流的性质与弱耦合RG RG分析获得的临界点相同。这与许多粒子纠缠中的相变相吻合，因为纠缠熵RG流量根据拓扑$θ$ term的值显示了临界和间隙阶段的不同特征。我们演示了包含EHM网络的多体征态的Ryu-takyanagi熵结合，具体化了与全息二元性原理的关系。熵结合的缩放还区分了间隙和无间隙的相位，这意味着在整个临界点上产生了非常不同的全息空间。最后，我们将费米表面视为与高能电子状态耦合的量子杂质。为了研究通过隔离杂质产生的纠缠熵而设计的经验，并提出了通过研究完整计数统计量的量子噪声和高阶累积物来测量它的方法。
We perform a unitary renormalization group (URG) study of the 1D fermionic Hubbard model. The formalism generates a family of effective Hamiltonians and many-body eigenstates arranged holographically across the tensor network from UV to IR. The URG is realized as a quantum circuit, leading to the entanglement holographic mapping (EHM) tensor network description. A topological $Θ$-term of the projected Hilbert space of the degrees of freedom at the Fermi surface are shown to govern the nature of RG flow towards either the gapless Tomonaga-Luttinger liquid or gapped quantum liquid phases. This results in a nonperturbative version of the Berezenskii-Kosterlitz-Thouless (BKT) RG phase diagram, revealing a line of intermediate coupling stable fixed points, while the nature of RG flow around the critical point is identical to that obtained from the weak-coupling RG analysis. This coincides with a phase transition in the many-particle entanglement, as the entanglement entropy RG flow shows distinct features for the critical and gapped phases depending on the value of the topological $Θ$-term. We demonstrate the Ryu-Takyanagi entropy bound for the many-body eigenstates comprising the EHM network, concretizing the relation to the holographic duality principle. The scaling of the entropy bound also distinguishes the gapped and gapless phases, implying the generation of very different holographic spacetimes across the critical point. Finally, we treat the Fermi surface as a quantum impurity coupled to the high energy electronic states. A thought-experiment is devised in order to study entanglement entropy generated by isolating the impurity, and propose ways by which to measure it by studying the quantum noise and higher order cumulants of the full counting statistics.
